$A$ conductor lies parallel to the $Z$-axis between $-1.5 \le Z < 1.5 \text{ m}$,carrying a constant current of $10.0 \text{ A}$ in the $-\hat{a}_z$ direction. For the given magnetic field $\vec{B} = 3.0 \times 10^{-4} e^{-0.2x} \hat{a}_y \text{ T}$,find the power required to move the conductor at a constant speed from $x = 0$ to $x = 2.0 \text{ m}$ in a time interval of $5 \times 10^{-3} \text{ s}$. Assume the motion is parallel to the $X$-axis. ........... $\text{W}$

$A$ proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively,then the region of space may have :
$(A)$ $E=0, B=0$
$(B)$ $E=0, B \neq 0$
$(C)$ $E \neq 0, B=0$
$(D)$ $E \neq 0, B \neq 0$
Choose the most appropriate answer from the options given below :

Which of the following statements is correct?

Two parallel long wires carry currents $i_1$ and $i_2$ with $i_1 > i_2$. When the currents are in the same direction,the magnetic field midway between the wires is $10 \, \mu T$. When the direction of $i_2$ is reversed,it becomes $40 \, \mu T$. The ratio $i_1/i_2$ is

Six point charges,each of magnitude $q$,are arranged in different manners as shown in the image. In each case,a point $M$ and a line $PQ$ passing through $M$ are shown. Let $E$ be the electric field and $V$ be the electric potential at $M$ (potential at infinity is zero) due to the given charge distribution when it is at rest. Now,the whole system is set into rotation with a constant angular velocity about the line $PQ$. Let $B$ be the magnetic field at $M$ and $\mu$ be the magnetic moment of the system in this condition. Assume each rotating charge to be equivalent to a steady current. Match the conditions in Column $I$ with the configurations in Column $II$.

Column $I$	Column $II$
$(A)$ $E=0$	$(p)$ Charges at corners of a regular hexagon. $M$ is the centre. $PQ$ is perpendicular to the plane.
$(B)$ $V \neq 0$	$(q)$ Charges on a line perpendicular to $PQ$ at equal intervals. $M$ is the mid-point.
$(C)$ $B=0$	$(r)$ Charges on two coplanar concentric rings. $M$ is the common centre. $PQ$ is perpendicular to the plane.
$(D)$ $\mu \neq 0$	$(s)$ Charges at corners and mid-points of a rectangle. $M$ is the centre. $PQ$ is parallel to the longer sides.
	$(t)$ Charges on two coplanar,identical rings. $M$ is the mid-point between centres. $PQ$ is perpendicular to the line joining centres.

An $\alpha$ particle of energy $10 \ eV$ is moving in a circular path in a uniform magnetic field. The energy of a proton moving in the same path and the same magnetic field will be [mass of $\alpha$ particle $= 4 \times$ mass of proton]. (in $eV$)